Yield Enhancement of Reconﬁgurable Microﬂuidics-Based...

Yield Enhancement of ReconfigurableMicrofluidics-Based Biochips UsingInterstitial Redundancy

FEI SU and KRISHNENDU CHAKRABARTY

Duke University

Microfluidics-based biochips for biochemical analysis are currently receiving much attention. They

automate highly repetitive laboratory procedures by replacing cumbersome equipment with minia-

turized and integrated systems. As these microfluidics-based microsystems become more complex,

manufacturing yield will have significant influence on production volume and product cost. We

propose an interstitial redundancy approach to enhance the yield of biochips that are based on

droplet-based digital microfluidics. In this design method, spare cells are placed in the interstitial

sites within the microfluidic array, and they replace neighboring faulty cells via local reconfig-

uration. The proposed design method is evaluated using a set of concurrent real-life bioassays.

The defect-tolerant design approach based on space redundancy and local reconfiguration is ex-

pected to facilitate yield enhancement of microfluidics-based biochips, especially for the emerging

marketplace.

Categories and Subject Descriptors: B.7.2 [Integrated Circuits]: Design Aids—Placement androuting; B.8.1 [Performance and Reliability]: Reliability, Testing, and Fault-Tolerance; J.3 [Lifeand Medical Sciences]—Biology and genetics, health

General Terms: Algorithms, Performance, Design, Reliability

Additional Key Words and Phrases: Microfluidics, yield enhancement, reconfiguration, space

redundancy

1. INTRODUCTION

Microfluidics-based biochips promise to revolutionize clinical diagnostics, DNAsequencing, and other procedures involving molecular biology [Verpoorte andRooij 2003]. In contrast to continuous-flow microfluidic biochips consisting ofpermanently etched micropumps, microvalves, and microchannels [Verpoorteand Rooij 2003], droplet-based microfluidic biochips relying on the manipula-tion of individual droplets through electrowetting and referred to as digital

The research work was supported by the National Science Foundation under grant number IIS-

0312352. A preliminary and abridged version of this article was published in Proceedings of Design,Automation and Test in Europe Conference, 2005.

Authors’ address: Department of Electrical and Computer Engineering, Duke University, Durham,

NC 27708; email: {fs,krish}@ee.duke.edu.

Permission to make digital or hard copies of part or all of this work for personal or classroom use is

granted without fee provided that copies are not made or distributed for profit or direct commercial

advantage and that copies show this notice on the first page or initial screen of a display along

with the full citation. Copyrights for components of this work owned by others than ACM must be

honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers,

to redistribute to lists, or to use any component of this work in other works requires prior specific

permission and/or a fee. Permissions may be requested from Publications Dept., ACM, Inc., 1515

Broadway, New York, NY 10036 USA, fax: +1 (212) 869-0481, or [email protected]© 2006 ACM 1550-4832/06/0400-0104 $5.00

ACM Journal on Emerging Technologies in Computing Systems, Vol. 2, No. 2, April 2006, Pages 104–128.

Yield Enhancement of Microfluidics-Based Biochips • 105

microfluidics, have recently been demonstrated [Pollack et al. 2000]. Digitalmicrofluidics offer dynamic reconfigurability, whereby groups of cells in a mi-crofluidic array can be reconfigured to change their functionality during the con-current execution of a set of bioassays. These features make digital microfluidicsa promising platform for massively-parallel DNA analysis, automated drug dis-covery, and real-time biomolecular recognition.

Future advances in fabrication technology will allow increased integrationof microfluidic components in composite microsystems. The 2003 InternationalTechnology Roadmap for Semiconductors (ITRS) anticipates that microfluidicbiochips will soon be integrated with electronic components in system-on-chip(SOC) design. It is expected that several bioassays will then be concurrentlyexecuted in a single microfluidic array [Srinivasan et al. 2003]. However, as inthe case of integrated circuits, an increase in density and area of microfluidics-based biochips will reduce yield, especially for new technology nodes. Low yieldis a deterrent to large scale and high-volume production, and it tends to in-crease production cost. It will take time to ramp up yield-learning based onan understanding of defect types in such mixed-technology SOCs. Therefore,defect-tolerant designs are especially important for the emerging marketplace.

Yield enhancement through space redundancy and reconfiguration hasbeen successfully applied to memories, processor arrays (PAs), and field-programmable gate arrays (FPGAs) [Koren and Koren 1998; Howard et al.1994]. The success of these techniques can be attributed to the high regular-ity of memories, PAs, and FPGAs and the ease with which they can be testedand reconfigured to avoid faulty elements. Digital microfluidics-based biochipsare also amenable to redundancy-based yield enhancement. As in the case ofmemories, they contain regular arrays of small elements, and these elementsare simple and identical. Similar to FPGAs, reconfigurability is an inherentproperty of these devices.

In this article, we propose a scheme for incorporating defect tolerance inthe design of digital microfluidics-based biochips. While spare rows/columnsaround a mesh-connected array are often used in fault-tolerant processor ar-rays and FPGAs [Howard et al. 1994], the property of fluidic locality preventsthe application of this simple redundancy technique to microfluidic biochips.Due to the absence of programmable interconnects such as switches betweenmicrofluidic cells, a droplet is only able to move directly to the adjacent cells.Thus, a faulty cell can only be replaced by its physically adjacent cells. Con-sequently, a complicated shifted replacement process is required to utilize thespare cells located in the boundary row/column; this results in an unacceptableincrease in the reconfiguration cost.

We propose an interstitial redundancy approach to address this problem.In this approach, spare cells are placed in the interstitial sites within themicrofluidic array such that a spare cell can functionally replace any faultycells that are physically adjacent to it. This defect tolerance method owesits effectiveness to the high utilization of local reconfiguration. We applythis space redundancy technique to a new biochip design with hexagonalelectrodes. Microfluidic biochips with different levels of redundancy canbe designed to target given yield levels and manufacturing processes. We

ACM Journal on Emerging Technologies in Computing Systems, Vol. 2, No. 2, April 2006.

106 • F. Su and K. Chakrabarty

introduce a metric called effective yield to evaluate the yield enhancementprovided by these defect-tolerant designs. A set of real-life bioassays, thatis, multiplexed in-vitro diagnostics on human physiological fluids, is usedto evaluate the proposed method. Simulation results show that the yield ofa digital microfluidics-based biochip can be significantly increased with theaddition of interstitial redundancy and the use of local reconfiguration.

The organization of the remainder of the article is as follows. In Section 2,we discuss related prior work. Section 3 presents an overview of digitalmicrofluidics-based biochips. It also introduces a new design based on hexago-nal electrodes. Section 4 discusses manufacturing defects in digital microfluidicbiochips. Section 5 presents a unified test methodology. Reconfiguration tech-niques for microfluidic biochips are also presented. In Section 6, we introducevarious defect-tolerant designs with different levels of redundancy. The defecttolerance of these designs is evaluated in Section 7. In Section 8, multiplexedin-vitro diagnostics on human physiological fluids is used to evaluate theproposed yield improvement methodology. Finally, conclusions are drawn inSection 9.

2. RELATED PRIOR WORK

Defect-tolerance techniques have been successfully used for memory chips sincethe late 1970’s [Koren and Koren 1998]. In contrast to memory arrays, few logiccircuits have been designed with built-in redundancy. The absence of regularityin these circuits usually leads to high overhead. Regular circuits, such as proces-sor arrays and FPGAs, require less redundancy; a number of defect-tolerancetechniques have been proposed to enhance their yield [Howard et al. 1994;Singh 1988].

Microelectromechanical systems (MEMS) is a relatively young field com-pared to integrated circuits. It employs micromachining techniques, such assurface micromachining and bulk micromachining, in the fabrication process[Madou 1997]. These processes are less mature than standard CMOS manu-facturing processes. As a result, the yield for MEMS devices is often less thanthat for integrated circuits. Attempts have been made in recent years to makeMEMS defect tolerant. For example, design-for-manufacturing has been incor-porated into the design process for MEMS [Dewey et al. 2000].

Microfluidics differs from MEMS in the underlying energy domains and inthe working principles. Hence, defect, tolerance techniques for MEMS cannotbe directly applied to microfluidic biochips. Recently a comprehensive cost-effective test methodology for digital microfluidics-based biochips was proposedin Su et al. [2003, 2005]. Faults are classified as either manufacturing or opera-tional, and techniques have been developed to detect these faults by electricallycontrolling and tracking the droplet motion. Based on the detection mechanism,an efficient concurrent testing scheme that interleaves test application with aset of bioassays was also proposed in Su et al. [2004]. These testing techniquescan be further integrated with system-level CAD tools to facilitate design-for-test (DFT) and defect tolerance for digital microfluidics-based biochips [Su andChakrabarty 2005].



Fig. 1. (a) Basic cell used in a digital microfluidics-based biochip; (b) top-view of microfluidic array.

3. DIGITAL MICROFLUIDICS-BASED BIOCHIPS

Digital microfluidics-based biochips manipulate nanoliter-volume dropletsusing electrowetting. The basic cell in a digital microfluidics-based biochipconsists of two parallel glass plates, shown in Figure 1(a). The bottom platecontains a patterned array of individually controllable electrodes, and the topplate contains a ground electrode. The droplets containing biomedical samplesare sandwiched between these two plates and surrounded by a filler mediumsuch as silicone oil. In addition, the droplets are insulated from the electrodearray by Parylene C (∼800nm), and a thin layer of hydrophobic Teflon AF 1600(∼50nm) is coated onto the top and bottom plates to decrease the wettability ofthe surface.

Electrowetting is the basic principle of microdroplet transportation whereinthe interfacial tension of a droplet is modulated with an electric field. Acontrol voltage is applied to an electrode adjacent to the droplet and, at thesame time, the electrode just under the droplet is deactivated. Thus, an accu-mulation of charge in the droplet/insulator interface over the activated electroderesults in a surface tension gradient, which consequently causes the transporta-tion of the droplet. By varying the electrical potential along a linear array ofelectrodes, nanoliter-volume droplets can be transported along this line of elec-trodes. The velocity of the droplet can be controlled by adjusting the controlvoltage (0 ∼ 90V), and droplets have been observed with velocities up to 20cm/s[Pollack et al. 2002]. Furthermore, based on this principle, microdroplets canbe transported freely to any location on a two-dimensional array without theneed for pumps and valves. The configurations of the microfluidic array areprogrammed into a microcontroller that controls the voltages of electrodes inthe array. A generic digital microfluidics-based biochip consists of a basic mi-crofluidic platform, which moves and mixes droplets containing biochemicalsamples and reagents, several reservoirs that store and generate the dropletsof samples and reagents, and an integrated optical detection system consistingof LEDs and photodiodes (see Figure 1(b)).

In the latest generation of microfluidic biochips, hexagonal electrodes are be-ing used to replace the conventional square electrodes design; this close-packeddesign is expected to increase the effectiveness of droplet transportation in a2D array. The top view of a microfluidic array with hexagonal electrodes isshown in Figure 2(a). A droplet can be moved to an adjacent cell in six possibledirections. Recently, printed circuit board (PCB) technology has been used to



Fig. 2. (a) Digital microfluidics-based biochip with hexagonal electrodes; (b) fabricated PCB-based

microfluidic array.

replace the conventional glass plate as the substrate with the aim of reducingmanufacturing cost [Dewey et al. 2000]. Figure 2(b) shows an image of sucha fabricated microfluidic array with 10 × 10 hexagonal electrodes. In this ar-ticle, we attempt to make this hexagonal array defect tolerant through spaceredundancy and local reconfiguration.

4. MANUFACTURING DEFECTS

Digital microfluidics-based biochips are fabricated using standard microfab-rication techniques, the details of which are described in Pollack [2001]. Mi-crofluidic biochips exhibit behavior resembling that of analog and mixed-signaldevices. Therefore, we can classify faults caused by the manufacturing defectsas being either catastrophic or parametric, along the lines of fault classificationfor analog circuits [Jee and Ferguson 1993]. Catastrophic (hard) faults lead toa complete malfunction of the system, while parametric (soft) faults cause adeviation in system performance. A parametric fault is detectable only if thisdeviation exceeds the tolerance in system performance. However, due to the un-derlying mixed technology and multiple energy domains, microfluidic biochipsexhibit failure mechanisms and defects that are significantly different fromfailure modes in integrated circuits.

Catastrophic faults may be caused by the following manufacturing defects.

—Dielectric breakdown. The breakdown of the dielectric at high voltage levelscreates a short between the droplet and the electrode. When this happens,the droplet undergoes electrolysis preventing further transportation.

—Short between adjacent electrodes. If a short occurs between two adjacentelectrodes, the two electrodes shorted effectively form one longer electrode.When a droplet resides on this electrode, it cannot overlap its adjacent elec-trodes. As a result, the actuation of the droplet can no longer be achieved.

—Degradation of the insulator. This degradation effect is unpredictable andmay become apparent gradually during the operation of the microfluidicsystem. Figure 3 illustrates the electrode degradation due to an insulatordegradation defect [Pollack 2001]. A consequence of insulator degradation isthat droplets often fragment and their motion is prevented because of theunwanted variation of surface tension forces along their flow path.



Fig. 3. Top view of a faulty unit cell: electrode degradation.

—Open in the metal connection between the electrode and the control source.This defect results in a failure in activating the electrode for transport.

Manufacturing defects that cause parametric faults include geometricalparameter deviations. The deviation in insulator thickness, electrode lengthand height between parallel plates may exceed their tolerance value duringfabrication.

The level of system integration and the design complexity of digitalmicrofluidics-based biochips are expected to increase in the near future dueto the growing need for high-throughput biochemical analysis on a chip. How-ever, shrinking processes, new materials, and the underlying multiple energydomains will make these biochips more susceptible to manufacturing defects.Moreover, some manufacturing defects are expected to be latent, and they maymanifest themselves during field operation of the biochips. In addition, harshoperational environments may introduce physical defects such as particle con-tamination during field operation. Consequently, robust testing techniques arerequired to ensure system dependability as biochips are deployed for safety-critical applications. Examples of such applications include field diagnostic in-struments to monitor infectious diseases and biosensors to detect biochemicaltoxins and other pathogens.

5. TESTING AND RECONFIGURATION TECHNIQUES

In the proposed testing methodology, test stimuli droplets containing the nor-mal conductive fluid (e.g., 0.1M KCL) are released into a two-dimensional mi-crofluidic array from on-chip reservoirs and are guided through the system fol-lowing the designed testing scheme. Both catastrophic and parametric faultsare detected by electrically controlling and tracking the motion of these teststimuli droplets. This testing method is minimally invasive and easy to im-plement, thus it alleviates the need for expensive and bulky external testingdevices.

To facilitate an efficient decision-making process, a unified detection mecha-nism is needed for both catastrophic and parametric faults [Su et al. 2003]. Theproposed unified detection mechanism consists of a simple RC oscillator cir-cuit formed by the sink electrodes and the fluid between them as an insulator;see Figure 4. The capacitance of this structure depends on the presence of the



Fig. 4. Simple RC oscillator circuit.

droplet since the filler medium and the droplet have distinct permittivities. Bysensing the capacitance of this structure using a simple frequency counter, onecan determine whether a droplet has reached the sink. This mechanism can beelectronically implemented and easily integrated on-chip. In order to provide aunidirectional and unambiguous detection mechanism, the pass/fail criterionhas to be determined based on the presence of the droplet at the sink electrode,and this criterion should be applied for all test cases. In the proposed testingscheme, we associate the fault-free operation with the presence of the dropletat the sink electrode and faulty operation with its absence.

Most catastrophic faults cause a complete cessation of droplet transportationat the system level. Therefore, we can easily detect these faults by using thetesting scheme outlined in Figure 5. The fault site in this microfluidic array ishighlighted. Droplets are first driven along one direction, for example, alongthe x-axis, and they are observed at the other end of the array. Each row ofthe array transports a single droplet of fluid. Due to the catastrophic fault inRow 3, no droplet is observed for this row. As a result, the cells in this row aredeemed as candidate faulty cells. Next, droplets are driven following the pathalong the y-axis, and due to the fault in the array, no droplet is observed at theother end of Column 3. Thus we conclude that the path of Column 3 containsa faulty cell. From the information about the faulty row and column, we canuniquely identify the faulty cell in the array.

This illustration assumes that a catastrophic fault affects only one cell ofthe array. The testing technique described here can, however, be extended forlocating multiple faulty cells, for example, through the use of multistep adap-tive fault location methods, and it can also be extended for the detection ofparametric faults [Su et al. 2003]. An important advantage of this approachis that it can be integrated into the droplet-manipulation-based microfluidicsteps underlying a biochemical reaction, for example, polymerase chain reac-tion. Concurrent testing can be carried out simultaneously with a bioassayby utilizing unused cells in the array, and a degree of fault tolerance can be



Fig. 5. Illustration of the fault testing scheme.

achieved by reconfiguring the array such that the droplets avoid faulty cells intheir flow paths [Su et al. 2004].

The reconfigurability inherent in digital microfluidics-based biochips can beused to increase production yield through production time reconfiguration tobypass manufacturing faults. In this scenario, we assume that a microfluidicbiochip has been fabricated along the lines of a reconfigurable array-baseddesign. Defective cells are identified using testing techniques prior to field de-ployment [Su et al. 2005a, 2005b]. Based on the defect map thus obtained,the configuration of the microfluidic array is changed in such a way that thefunctionality of the bioassays is not compromised. A similar scheme can beutilized to achieved, longer system lifetime through online reconfiguration toavoid operational faults. Once the concurrent testing procedure determines thefaulty status of biochips [Su et al. 2004], the operation of the normal bioassayis stopped. Then reconfiguration techniques are applied to tolerate faults andincrease system reliability.

The reconfiguration approaches can be divided into two categories. The firstcategory consists of techniques that do not add space redundancy, that is,spare cells, to the microfluidic array. Instead, they attempt to tolerate the de-fect by using fault-free unused cells. In order to achieve satisfactory yield us-ing this method, fault tolerance must be considered in the design procedure,for example, in the placement of microfluidic modules in the array [Su andChakrabarty 2005]. Consequently, it leads to an increase in design complexity.The second category of reconfiguration techniques is application-independentbecause it incorporates physical redundancy in the microfluidic array. Built-inspare cells can be utilized to replace a defective cell. Since a faulty cell is re-placed by a neighboring spare cell, these techniques are also referred to as localreconfiguration.



Fig. 6. Example of a microfluidic array with one single spare row.

6. DEFECT-TOLERANT DESIGNS WITH DIFFERENT REDUNDANCY LEVELS

There are several ways to include spare cells in a defect-tolerant microfluidic ar-ray. The first approach is to include spare rows/columns around the microfluidicarray. This is a common redundancy technique for PAs and FPGAs. However,in contrast to these electronic arrays with well-defined roles of logic blocks andinterconnect, cells in a microfluidic array can be used for storage, transport,or other functional operations on droplets. Due to the absence of separate in-terconnect entities, droplets can only move to physically adjacent cells. Thisproperty is referred to as microfluidic locality. Consequently, the functionalityof a faulty cell can only be assumed by its physically-neighboring cells in thearray. Microfluidic locality limits the reconfiguration capabilities of the sparerows/columns if they are not adjacent to the faulty cell. In order to utilize thespare cell in the boundary rows/columns, a series of replacement, referred toas shifted replacement is required. In shifted replacement, each faulty cell isreplaced by one of its fault-free adjacent cells which is, in turn, replaced by oneof its adjacent cells, and so on, until a spare cell from the boundary is incor-porated in the reconfigured structure. In many cases, this shifted replacementprocedure will not only involve the faulty module, but it will also require thereconfiguration of fault-free modules. Therefore, it significantly increases thecomplexity of the reconfiguration. Figure 6 shows an example of a microfluidicarray with a single spare row. If one cell in Module 1 is faulty, Module 1 can onlybe relocated to bypass the faulty cell, while other modules remain unchanged;see Figure 6(b). However, if there is one faulty cell in Module 3, the shiftedreplacement of Module 3 causes the reconfiguration of Module 2 even thoughit is fault-free; see Figure 6(c).

In order to address the problems resulting from microfluidic locality, a newspace redundancy approach termed interstitial redundancy [Singh 1988], is pro-posed in this article. In this approach, spare cells are located in the interstitialsites within the microfluidic array such that each spare cell is able to function-ally replace any one of the primary cells adjacent to it. In contrast to redundancybased on boundary spare rows/columns, interstitial redundancy offers a simplereconfiguration scheme that effectively utilizes local reconfiguration. We applyinterstitial redundancy to a digital microfluidics-based biochip with hexagonal



Fig. 7. Top view and graph model of DTMB(1, 6).

electrodes. Such defect-tolerant microfluidic arrays can incorporate differentlevels of redundancy depending on the number and location of spare cells. Wenext introduce some key definitions.

Definition 1. A defect-tolerant design for a digital microfluidics-basedbiochip, denoted DTMB(s, k), has interstitial spare cells such that eachnonboundary primary cell can be replaced by any one of s spare cells, and eachnonboundary spare cell can be used to replace any one of k primary cells.

Definition 2. The redundancy ratio (RR) for a defect-tolerant microfluidicarray with interstitial redundancy is the ratio of the number of spare cells inthe array to the number of primary cells. Clearly, for a DTMB(s, k) array oflarge size, RR ≈ s/k.

A DTMB(1, 6) design is shown in Figure 7(a). A corresponding graph model,derived from the array, is shown in Figure 7(b). White nodes in the graph rep-resent the primary cells in the microfluidic biochip, while black nodes denotespare cells. An edge between two nodes indicates that the two cells representedby these nodes are physically adjacent in the array. Each primary cell is adja-cent to only one spare cell, and every spare cell is adjacent to six primary cells.Therefore, the redundancy ratio for this array approaches 0.1667 as the arraysize increases.

Other defect-tolerant array designs, for example, DTMB(2, 6), DTMB(3, 6)and DTMB(4, 4), are shown in Figures 8–10. The redundancy ratios of thedifferent designs are listed in Table I.

7. ESTIMATION OF YIELD ENHANCEMENT

The effectiveness of various defect-tolerant designs can be determined by esti-mating their enhanced yields. Here the yield is defined as the percentages ofdefect-tolerant biochips after manufacturing (including fault-free chips as wellas the defective chips that can be successfully reconfigured to avoid defects).The yield analysis in this article is based on the following assumption.



Fig. 8. DTMB(2, 6) designs.

Fig. 9. An DTMB(3, 6) design.

Fig. 10. An FTMB(4, 4) design.



Table I. Redundancy Ratios for Different Defect-Tolerant Architectures

Design DTMB(1, 6) DTMB(2, 6) DTMB(3, 6) DTMB(4, 4)

RR 0.1667 0.3333 0.5000 1.0000

Fig. 11. Illustration of clusters for DTMB(1,6) array.

Assumption. Each single cell in the microfluidic array, including each pri-mary and spare cell, has the same defect probability q. Moreover, the fail-ures of the cells are independent. Let p = 1 − q denote the survivalprobability.

Note that the assumption of equal survival probabilities is reasonable sinceeach cell in the microfluidic array has the same structure. In addition, the as-sumption of independent failures is valid for random and small spot defectswhich result from imperfect materials and from undesirable chemical and air-borne particles.

Based on these assumptions, the yield for a defect-tolerant design can beobtained in terms of p. We use both analytical modeling and Monte-Carlosimulation.

Since each primary cell is physically adjacent to only one spare cell inDTMB(1, 6), the spare assignment to a faulty cell is straightforward. Thus,its yield can be easily obtained analytically. We can view DTMB(1, 6) as a com-position of identical clusters that consist of one spare cell and six primary cellssurrounding the spare cell as shown in Figure 11. The yield Yc of any clusterin DTMB(1, 6) is determined by the likelihood of having at most one failed cellamong these seven cells, that is,

YC = p7 + 7p6(1 − p).

A biochip with n primary cells can be approximately divided into n/6 clusters.Since the cluster failures are independent, the yield Y for this design is givenby

YDTMB(1,6) = Y n/6C = (p7 + 7p6(1 − p))n/6.



Fig. 12. Estimated yield for DTMB(1,6).

Figure 12 shows the yield for DTMB(1, 6) for different values of p and n, andcompares it to the yield for a biochip without redundancy. Clearly, interstitialredundancy improves the yield of the microfluidic biochip.

For the defect-tolerant design with a higher level of redundancy such asDTMB(2, 6) and DTMB(3, 6), analytical modeling to determine the yield is notas straightforward as in DTMB(1, 6) due to the more complicated spare as-signments. However, we can still apply the cluster-based method in an attemptto estimate the yield of these defect-tolerant array designs. For example, fora DTMB(2, 6) array, we can envision it to consist of identical clusters; eachcluster comprises two spare cells and six primary cells following the definitionof DTMB(2, 6), that is, each primary cell can be replaced by any one of twospare cells, and each spare cell can be used to replace any one of six primarycells. The graph model of such a cluster in DTMB(2, 6) is shown in Figure 13(a)where an edge between white nodes (representing the primary cells) and blacknodes (denoting spare cells) indicates that the primary cell can be replaced bythe spare cell. Actually we can view a partition consisting of two neighboringspare cells and their surrounding primary cells in the microfluidic array as aphysical representation of the proposed cluster as shown in Figure 13(b). Notethat, since the boundary primary cells are shared by two adjacent partitions,we consider only six (i.e., 10/2 + 1) primary cells in a cluster model.

The survival probability of a DTMB(2, 6) cluster is the likelihood of havingat most two defective cells among these eight cells, that is,

YC = p8 + 8p7(1 − p) + 28p6(1 − p)2.

We also assume that a DTMB(2, 6) array with n primary cells can be approx-imately divided into n/6 clusters, and the failures of the different clusters areindependent. The yield Y for this design is then estimated by

YDTMB(2,6) = Y n/6C = (p8 + 8p7(1 − p) + 28p6(1 − p)2)n/6.



Fig. 13. (a) Graph model for a DTMB(2, 6) cluster; (b) illustration of clusters for the DTMB(2,6)

array.

Fig. 14. Estimated yield for DTMB(2,6).

The simulation results on yield estimation for DTMB(2, 6) arrays with dif-ferent sizes are shown in Figure 14. A similar analytical modeling method canalso be applied to DTMB(3, 6) designs as shown in Figure 15; their yields canbe estimated by

YDTMB(3,6) = Y n/6C = (p9 + 9p8(1 − p) + 36p7(1 − p)2 + 84p8(1 − p))n/6.



Fig. 15. (a) Graph model for a DTMB(3, 6) cluster; (b) illustration of clusters for DTMB(3,6) array.

Fig. 16. A maximal bipartite matching graph model.

We can also estimate the yield for a defect-tolerant design using Monte-Carlosimulation. During each run of the simulation, the cells in the microfluidic ar-ray, including both primary and spare cells, are randomly chosen to fail withprobability p. We then check if these defects can be tolerated via local reconfig-uration based on the interstitial spare cells. This checking procedure is basedon a graph matching approach as described in the following.

We develop a bipartite graph model to represent the relationship betweenfaulty and spare cells in the microfluidic array. A bipartite graph BG(A, B, E) isa graph whose nodes can be partitioned into two sets, A and B, and each edge inE has one node in A and one node in B [Su et al. 2003]. In our model, nodesin A represent the faulty primary cells in the microfluidic array, while nodesin B denote the fault-free spare cells. An edge exists from a node a in A to anode b in B if and only if the faulty primary cell represented by a is physicallyadjacent to the spare cell represented by b. An example of a bipartite graphmodel is shown in Figure 16. A matching M of a bipartite graph BG(A, B, E) is



Fig. 17. Example of using maximal bipartite matching model to determine reconfigurability.

a subset of the edges (M ⊆ E) with the property that no two edges of Msharethe same node. Edges in M are called matched edges, while the other edgesare free. If [a, b] is a matched edge, then a is the mate of b. Nodes that are notincident upon any matched edge are celled exposed vertices, while the othersare called matched vertices. A path Pt = [u1, u2, . . . , uk], where ui ∈ A ∪ B, iscalled alternating if [u1, u2], [u3, u4], . . . [u2 j−1, u2 j ], . . . are free whereas [u2,u3], [u4, u5], . . . [u2 j , u2 j+1], . . . are matched. We further call an alternating pathPt = [u1, u2, . . . , uk] an augmenting path if both u1 and uk are exposed vertices.

A maximal matching for this bipartite graph model can be obtained usingwell-known techniques that are based on a theorem stated as follows:

THEOREM 1. A matching M in a graph is maximum if and only if there is noaugmenting path in this graph with respect to M [Asratian et al. 1998].

The key idea underlying the algorithm is to start with any matching (e.g., theempty one), and repeatedly search for augmenting paths to augment the match-ing. The search stops when there is no augmenting path, and then a maximummatching Mmax is found. If this maximal matching Mmax covers all nodes in A,it implies that all faulty cells can be replaced by their adjacent fault-free sparecells through local reconfiguration; an example is shown in Figure 17(a). Other-wise, this microfluidic biochip cannot be reconfigured as shown in Figure 17(b).After a large number of simulation runs, the yield of this microfluidic array isdetermined from the proportion of successful reconfigurations. The pseudocodefor the proposed matching-based Monte-Carlo method is shown in Figure 18.The simulation results for DTMB(2, 6), DTMB(3, 6) and DTMB(4, 4) by the



Fig. 18. Pseudocode of Monte-Carlo simulation method for yield estimation.

Fig. 19. Yield estimation for DTMB(2,6), DTMB(3,6) and DTMB(4,4).

Monte-Carlo method are shown in Figure 19 where n is the number of primarycells.

We also compare the yield estimation obtained using analytical modeling andMonte-Carlo simulation methods; an example of the comparison for DTMB(2, 6)



Fig. 20. Comparison of yield estimation by two different methods.

Fig. 21. Effective yield for different levels of redundancy.

and DTMB(3, 6) designs is shown in Figure 20 which shows that the two esti-mates are close to each other.

From Figure 19, it is clear that a higher level of redundancy leads to ahigher yield. However, adding more redundant cells increases the array areaand thereby manufacturing cost. To measure yield enhancement relative to theincreased array size, we define the effective yield EY as:

EY = Y × (n/N ) = Y /(1 + RR),

where n is the number of primary cells, and N is the total number of cellsin the microfluidic array. The parameter EY represents the trade-off betweenyield enhancement and the increase in manufacturing cost. The variation ofEY with p for different redundancy levels is shown in Figure 21. The numberof primary cells is set to 100. As expected, the results show that a microfluidicstructure with the higher level of redundancy, such as DTMB(4, 4), is suitable



for small values of p. On the other hand, a lower level of redundancy, such asDTMB(1, 6) or DTMB(2, 6), should be used when p is relatively high.

Note that the yield analysis discussed thus far assumes that all primary cellsin the microfluidic array are used in the bioassay. However, in many practicalbiochip applications, not all primary cells are utilized by bioassays. The unusedprimary cells need not to be reconfigured even if they are defective. Thus ahigher value of the yield can be obtained if the array utilization is also consid-ered; we illustrate this issue with a real-life example in the next section. Wecan view the yield analysis results in this section as application-independentindexes which are used as a guideline for defect-tolerant biochip designs.

8. EXAMPLE: MULTIPLEXED IN-VITRO DIAGNOSTICS

In this section, we evaluate the proposed defect-tolerant design by applying itto a digital microfluidics-based biochip used for multiplexed biomedical assays.The in-vitro measurement of glucose and other metabolites, such as lactate,glutamate and pyruvate, in human physiological fluids plays a critical role inclinical diagnosis of metabolic disorders. For example, the change of regularmetabolic parameters in the patient’s blood can signal organ damage or dys-function prior to observable microscopic cellular damages or other symptoms.Recently, the feasibility of performing a colorimetric enzyme-kinetic glucoseassay on a digital microfluidic biochip has been successfully demonstrated inexperiments [Srinivasan et al. 2004].

The glucose assay performed on the biochip is based on Trinder’s reaction,a colorimetric enzyme-based method [Trinder 1969]. The enzymatic reactionsinvolved in the assay are:

Glucose + H2O + O2

GlucoseOxidase−−−−−−−−→ Gluconic Acid + H2O2,

2H2O2 + 4 − AAP + TOPSPeroxidase−−−−−→ Quinoneimine + 4H2O.

In the presence of Glucose oxidase, glucose can be enzymatically oxidizedto gluconic acid and hydrogen peroxide. Then, in the presence of peroxidase,the hydrogen peroxide reacts with 4-amino antipyrine (4-AAP) and N-ethyl-N-sulfopropyl-m-toluidine (TOPS) to form violet-colored quinoneimine which hasan absorbance peak at 545nm. Based on Trinder’s reaction, a complete glucoseassay can be performed following three steps, namely, transportation, mixing,and optical detection as shown in Figure 22. A sample droplet containing glu-cose and a reagent droplet containing glucose oxidase, peroxidase, 4-AAP, andTOPS, are dispensed into the microfluidic array from their respective dropletsources. They are then transported towards a mixer where the sample and thereagent droplets are mixed. The mixed droplet is transported onto a transpar-ent electrode in order to observe the absorbance of the products of the enzy-matic reaction. Absorbance measurements are performed with a green LEDand a photodiode. The glucose concentration can be measured from the ab-sorbance which is related to the concentration of colored quinoneimine in thedroplet. Besides glucose assays, other metabolites such as lactate, glutamate,and pyruvate have been detected in a digital microfluidic biochip recently. In



Fig. 22. Photos of different steps of a glucose assay carried out on a digital microfluidic biochip

[Srinivasan et al. 2004].

Fig. 23. Fabricated biochip used for multiplexed bioassays.

addition to current metabolites, a number of reagents can be added onto a chipto enable a multiplexed in-vitro diagnostics platform on different human phys-iological fluids. Figure 23 shows a recently fabricated microfluidic biochip usedfor multiplexed biomedical assays [Srinivasan et al. 2004]. In this biochip withsquare electrodes, SAMPLE1 and SAMPLE2 contain glucose and REAGENT1and REAGENT2 contain the reagents.

In this first design and demonstration, only cells used for the bioassays werefabricated; no spare cells were included in the array. Thus, even if one arbitrarycell in this biochip becomes faulty due to a manufacturing defect, this failurecannot be avoided by reconfiguration, and the fabricated biochip has to be dis-carded. Consequently, the yield for this biochip design is very low. It is only0.3378 even if the survival probability of a single cell is as high as 0.99. Suchlow yield makes the first biochip design unsuitable for future mass fabricationand use in clinic diagnostics.

In order to improve the yield, we use a defect-tolerant design with inter-stitial redundancy as described in Section 7. To facilitate the comparison, thetopological structure of primary cells in the first design is directly mapped to a



Fig. 24. A defect-tolerant design based on DTMB(2, 6).

Fig. 25. Estimated yield enhancement of DTMB(2, 6) design.

DTMB(2, 6) design. (Note that here DTMB(2, 6) is chosen for ease of illustration.The following analysis can be easily extended to other defect-tolerant arrayssuch as DTMB(1, 6) and DTMB(3, 6) designs.) The new defect-tolerant designhas the same number of primary cells used for multiplexed biomedical assays asthe original design, see Figure 24. There are 252 primary cells (108 of them usedin assays) and 91 spare cells in this defect-tolerant biochip. Figure 25 shows



Fig. 26. Yield estimation for the DTMB(2, 6)-based design in the presence of multiple defects.

the estimated yield of this defect-tolerant design by the Monte-Carlo methodfor different values of survival probability p of a single hexagonal electrode.Compared to the original design, the DTMB(2, 6) design leads to a significantlyhigher yield.

To further illustrate the improvement in yield, we randomly introduce m cellfailures, and then apply local reconfiguration to avoid them. The yield in thepresence of m failures is obtained through Monte-Carlo simulation. The yieldfor the different values of m is shown in Figure 26. For up to 35 faults, theredundant design can provide a yield of at least 0.90. An example of successfulreconfiguration in the presence of 10 faulty cells is shown in Figure 27.

In the DTMB(2, 6) design, although there are a total of 252 primary cellsin the array, only 108 primary cells are used in the biochemical application.The remaining primary cells can serve as spare cells or they can be used laterin a new set of remapped bioassays. This spare design has the advantage ofeasy droplet motion control since enough spacing between different dropletroutes prevents multiple droplets from being unintentionally mixed [Su et al.2006]. However, we can further map the design into a smaller array as shownin Figure 28. This new packed DTMB(2, 6) design has the same number (i.e.,108) of primary cells used in assay but with a much smaller array size (a totalof 196 cells, 43% less than the previous design). We next estimate the yieldfor these two different DTMB(2, 6) designs, see Figure 29. Note that the yieldfor the spare DTMB(2, 6) design is slightly higher than the packed design dueto more unused primary cells that need not be reconfigured. However, to takebiochip area overhead into account, we further analyze the effective yield forthese two designs, that is, EY = Y × (108/N ), where N is the total number ofcells in the microfluidic array. The simulation results in Figure 30 show that,for a relatively high value of survival probability p, the packed DTMB(2, 6)design is more suitable than the spare design when both yield enhancementand increase in manufacturing cost are considered.



Fig. 27. An example of local reconfiguration.

Fig. 28. A more packed defect-tolerant design based on DTMB(2, 6).

9. CONCLUSIONS

In this article, we have presented a yield enhancement technique for digitalmicrofluidics-based biochips. This technique relies on (i) space redundancy,whereby spare cells are placed in the interstitial sites of the microfluidic ar-ray, and (ii) local reconfiguration in which spare cells replace the neighboring



Fig. 29. Yield estimation for the spare and packed DTMB(2, 6) designs.

Fig. 30. Effective yield for the spare and packed DTMB(2, 6) designs.

faulty cells. The defect-tolerant design has been evaluated for a set of real-lifebioassays. Low yield, which is expected to be a consequence of increased areaand density of biochips, will be a deterrent to high-volume production and it willincrease production cost. The proposed defect-tolerant design approach for yieldenhancement will therefore be especially useful for the emerging marketplace.

ACKNOWLEDGMENTS

We thank Vamsee Pamula of Advanced Liquid Logic (http://www.liquid-logic.com) and William Hwang of Duke University for their help in this work.

REFERENCES

ASRATIAN, A. DENLEY, T., AND HAEGGKVIST, R 1998. Bipartite Graphs and Their Applications.

Cambridge University Press, NY, NY.



DEWEY, A. REN, H., AND ZHANG, T. 2000. Behavioral modeling of microelectromechanical systems

(MEMS) with statistical performance-variability reduction and sensitivity analysis. IEEE Trans.Circuits and Sys. II 47, 105–113.

HOWARD, N., TYRREL, A. AND ALLINSON, N. 1994. The yield enhancement of Field-Programmable

Gate Arrays. IEEE Trans. VLSI Syst. 2, 115–123.

International Technology Roadmap for Semiconductor (ITRS), http://public.itrs.net/Files/

2003ITRS/Home2003.htm.

JEE, A. AND FERGUSON, F. J. 1993. Carafe: An inductive fault analysis tool for CMOS VLSI circuits.

In Proceedings of the IEEE VLSI Test Symposium. 92–98.

KOREN, I. AND KOREN, Z. 1998. Defect tolerance in VLSI circuits: techniques and yield analysis,

In Proceedings of the IEEE. 86, 1819–1836.

MADOU, M. 1997. Fundamentals of Microfabrication. CRC Press, Boca Raton, FL.

PAPADIMITRIOU, C. AND STEIGLITZ, K. 1982. Combinatorial Optimization: Algorithms and Complex-

ity. Prentice-Hall, Englewood Cliffs, NJ.

POLLACK, M. 2001. Electrowetting-based microactuation of droplets for digital microfluidics, PhD

thesis, Duke University, Durham, NC.

POLLACK, M. G., SHENDEROV, A. D., AND FAIR, R. B. 2000. Electrowetting-based actuation of liquid

droplets for microfluidic applications. Appli. Physics Lett. 77, 1725–1726.

POLLACK, M. G., SHENDEROV, A. D., AND FAIR, R. B. 2002. Electrowetting-based actuation of droplets

for integrated microfluidics. Lab on a Chip 2, 96–101.

SINGH, A. 1988. Interstitial redundancy: an area efficient fault tolerance scheme for large area

VLSI processor arrays. IEEE Trans. Comput. 37, 1398–1410.

SRINIVASAN, V., PAMULA, V. K., AND FAIR, R. B. 2004. An integrated digital microfluidic lab-on-a-chip

for clinical diagnostics on human physiological fluids. Lab on a Chip 4, 310–315.

SRINIVASAN, V., PAMULA, V. K., POLLACK, M. G., AND FAIR, R. B. 2003. Clinical diagnostics on human

whole blood, plasma, serum, urine, saliva, sweat, and tears on a digital microfluidic platform. In

Proceedings μTAS. 1287–1290.

SU, F. AND CHAKRABARTY, K. 2005. Design of fault-tolerant and dynamically-reconfigurable mi-

crofluidic biochips. In Proceedings on Design, Automation and Test in Europe (DATE) Conference.

1202–1207.

SU, F., HWANG, W., AND CHAKRABARTY, K. 2006. Droplet routing in the synthesis of digital mi-

crofluidic biochips. Proceedings on Design, Automation and Test in Europe (DATE) Conference.

To appear.

SU, F., HWANG, W., MUKHERJEE, A., AND CHAKRABARTY, K. 2005. Defect-oriented testing and di-

agnosis of digital microfluidics-based biochips. In Proceedings of the IEEE International TestConference.

SU, F., OZEV, S., AND CHAKRABARTY, K. 2003. Testing of droplet-based microelectrofluidic systems.

In Proceedings of the IEEE International Test Conference. 1192–1200.

SU, F., OZEV, S., AND CHAKRABARTY, K. 2005. Ensuring the operational health of droplet-based

microelectrofluidic biosensor systems. IEEE Sensors 5, 763–773.

SU, F., OZEV, S., AND CHAKRABARTY, K. 2004. Concurrent testing of droplet-based microfluidic sys-

tems for multiplexed biomedical assays. In Proceedings of the IEEE International Test Conference.

883–892.

TRINDER, P. 1969. Determination of glucose in blood using glucose oxidase with an alternative

oxygen acceptor. Ann. Clinical Biochem. 6, 24–27.

VERPOORTE, E., AND DE, ROOIJ, N. F. 2003. Microfluidics meets MEMS. In Proceedings of the IEEE.91, 930–953.

Received October 2005; revised January, March 2006; accepted April 2006


Yield Enhancement of Reconﬁgurable Microﬂuidics-Based...

Documents

Transcript of Yield Enhancement of Reconﬁgurable Microﬂuidics-Based...